Internal energy Definition and 369 Threads

Homework Statement A closed, thermally-insulated box contains one mole of an ideal monatomic gas G in thermodynamic equilibrium with blackbody radiation B. The total internal energy of the system is ##U=U_{G}+U_{B}##, where ##U_{G}## and ##U_{B} (\propto T^4)## are the energies of the ideal gas...

I have question regarding the (W = ∫Pdv) formula for the work done during the expansion of an ideal gas and the change in internal energy during the process. If we were to have a gas enclosed inside an insulated cylinder with a movable piston at one end with cross sectional area "a", I...

This is from *Statistical Physics An Introductory Course* by *Daniel J.Amit* The text is calculating the energy of internal motions of a diatomic molecule. The internal energies of a diatomic molecule, i.e. the vibrational energy and the rotational energy is given by...

Homework Statement since specific heat c changes with temperature, but its treated as a constant in the heat formula, so that means that heat formula Q=mc(T2-T1) is just an approximation? correct? I see some texts define heat as Heat, q, is thermal energy transferred from a hotter system to a...

since specific heat c changes with temperature, but its treated as a constant in the heat formula, so that means that heat formula Q=mc(T2-T1) is just an approximation? correct? I see some texts define heat as Heat, q, is thermal energy transferred from a hotter system to a cooler system that...

Homework Statement Homework Equations The Attempt at a Solution v2=vf+x*vfg x =(0.4458-0.001067)/(0.71813-0.001067) =0.61973 u2=uf+x*ufg =535.08+0.61973*(2001.8-535.08) =1444.05kJ/kg ==> far different from solution! whats wrong with my attempt? thanks

Assuming all gases in the combustion reaction of benzoic acid (C6H5COOH) behave ideally, what is the "exact" change in internal energy? The context in which this question is being asked is after a calorimetry experiment. For all the intents and purposes of calorimetry, the change in internal...

The internal energy of monoatomic ideal gas is due to the kinetic energy of the molecules. Using Boltzmann Maxwell distribution, it is calculated that the kinetic energy due to translational motion of gas molecules of an ideal gas depends only on the temperature. In case of monoatomic gas, since...

Internal energy at a specific state can't be calculated but by kinetic theory of gases and law of equipartition of energy Average kinetic energy is directly proportional to temperature.And for an ideal gas internal energy is due to kinetic energy only for an ideal gas potential energy can be...

Homework Statement Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas but container B has twice the volume of container A. The internal energy of the gas in container B is (a) twice that for container A (b) the same as that for...

Integral constant for internal energy of ionic liquid I have a question, and I will be really grateful if someone helps me. I have a polynomial equation for internal energy which I calculated by integration an equation of state formula, which is based on density. But, because I calculated this...

Integral constant for internal energy of ionic liquid I have a question, and I will be really grateful if someone helps me. I have a polynomial equation for internal energy which I calculated by integration an equation of state formula, which is based on density. But, because I calculated this...

Hi, I've been reading about compressed air energy storage and keep coming across that in 300 bar containers the achievable energy is 0.1MJ/L. Is this 0.1MJ/L of the volume of the air it is compressed to or of the total L of air that was initially used? (E.g If 1500L is compressed to 300 bar...

Hi everyone! 1. Homework Statement Given is a function for the internal energy: ##U(T,V)=Vu(T)## Asked is to derive the entropy balance equation. In order to do so i need to find the "isothermal and adiabatic compressibility": $$\kappa_{T}=-\frac{1}{V}\left(\frac{\partial V}{\partial...

Homework Statement Please look at the below images which is the derivation of the relation between the internal energy of an ideal gas and the molar specific heat at constant volume. (Snaps taken from Fundamentals of Physics Textbook by David Halliday, Jearl Walker, and Robert Resnick) As...

Hello, I have some trouble understanding the virial expansion of the ideal gas. 1. Homework Statement I have given the state equation: $$ pV = N k_b T \left(1+\frac{A\left(T\right)}{V}\right) $$Homework Equations [/B] and a hint how to calculate the caloric equation of state $$...

Homework Statement Homework Equations Δu = ∫ [(a-Ru)+bT+cT^2+dT^3]dT The Attempt at a Solution The answer of 6447kJ/kmol is given but I am struggling to get to this answer after integrating the above formula and inserting the given values. Firstly would the integral of...

This is more of a recurring conceptual doubt that I keep on running into when solving thermodynamics problems. We are taught that variations between extensive state variables in equilibrium are given by the following 'fundamental formula': dE = TdS + \mathbf{J}\cdot{d}\mathbf{x} +...

Homework Statement Sketch a diagram of internal energy (y-axis) versus temperature in the range from -10°C to +112°C to indicate how energy would change for a fixed quantity of water in its three phrases. Label and explain the main features of the variation. Homework Equations The Attempt at...

Homework Statement [/B] Okay guys I have attached a picture of my work. I guess my question really is, if they are telling me that Cp =7/2 am I allowed to assume that I am dealing with a diatomic gas? If so, that would change my equation to (5/2) instead of (3/2) correct? and therefore my...

Homework Statement : [/B]Find the change in internal energy of 2kg water as it is heated from 0°C to 4°C. The specific heat capacity of water is 4200J/Kg and its densities at 0°C and 4°C are 999.9 kg/m3 and 1000kg/m3 respectively. Atm pressure=105PaHomework Equations :ΔU= Q-W W=PΔV M/V=D[/B]The...

Homework Statement I am trying to understand the law of conservation of energy from a very general perspective but coming across some issues. I am using the equation mentioned at end of this post, which is true for a system with no heat flows into or out of the system. In two situations...

Homework Statement A closed, rigid tank contains 2 kg of water, initially a two phase liquid–vapor mixture at T1 = 70°C. Heat transfer occurs until the tank contains only saturated vapor at T2 = 120C. Determine the heat transfer for the process, in kJ. answer choices: 3701kJ 119.4kJ 4835kJ...

Homework Statement Water is initially at P = 1 bar and T = 20°C. 100kg of water is pumped to a higher pressure at which P = 10 bar and T = 25°C. Find ΔU and ΔH Homework Equations H = m*h du = c*dT dh = c*dT + v*dP The Attempt at a Solution So far I have looked in my table and found that at P...

Homework Statement CO2 is at P=3atm, T = 295K and V=1.2m3. It is isobarically heated to T = 500K. Find ΔU and ΔH Homework Equations dU = cpdT The Attempt at a Solution I am having a hard time in general in this class. I understand that in this problem, ΔP = 0. Does this mean that there must...

According to the first law of thermodynamics, dQ = dU + dW and you can find dU = nCvdT If this is the case then when water at 100°C vaporizes to steam at 100°C shouldn't the change in internal energy be zero because it is dependent on temperature change?

Homework Statement What is the change in internal energy (in Joules) of an ideal gas that does 4.675x10^5J of work, while 2.95x10^6J of heat is transferred into the system and 7.95x10^6J of heat is transferred from the system to the environment? Calculate the change in temperature of the two...

Homework Statement We are asked to derive the expression for the internal energy of an ideal Fermi degenerate gas using Sommerfeld expansions, writing out terms up to the fourth order in ##(\frac{T}{T_F} )## , that is, we must determine ## \alpha ## in the following expression: $$ U=...

I've been given the following relations where as I understand it subindex 2 equals subindex e and subindex 1 equals subindex i: ***EDIT*** More accurately subindex 1; initial state of a control mass subindex 2: end state of a control mass (end state is simply state 2 in the problem at hand)...

Homework Statement Below, two experiments (1 and 2) are described, in which the same quantity of solid carbon dioxide is completely sublimated, at 25ºC: The process is carried out in a hermetically sealed container, non-deformable with rigid walls; The process is carried out in a cilinder...

This table is given in my book, $$\begin{array}[c!c!c!c!] \text{ }&\text{ Transitional }&\text{ Rotational }& \text{ Vibrational} \\ \hline \text{Linear molecules} & 3&2& 3N -5\\ \hline \text{Non-Linear molecules} & 3&3& 3N -6\\ \hline \end{array}$$ It is also given...

I am looking over the kinetic theory of gases. It is most commonly described as U = (3/2)*N*k*T = (3/2)*mass*R*T for a monatomic gas, assuming the gas is ideal. This is based on the derivation, where ultimately (3/2)*P*V = N*K = total kinetic energy of particles. My question, for a real gas...

Hi, As is commonly known, u = u(T,v) h = u(T,p) I've worked with some maths proofs of this a while ago, but do you guys have an intuitive way of understanding this without the maths, that is, why the state function for internal energy is defined by intensive volume and enthalpy with pressure...

We know, $$dU=TdS-PdV$$ ##\int PdV## can be calculated if the equation of state is given. I tried to express ##S## as a function of ##P ,V## or ##T## (any two of those). $$dS=\left(\frac{\partial S}{\partial V}\right)_T dV+\left(\frac{\partial S}{\partial T}\right)_V dT$$ $$=\left(\frac{\partial...

Homework Statement A uranium-238 atom can break up into a thorium-234 atom and a particle called an alpha particle, α-4. The numbers indicate the inertias of the atoms and the alpha particle in atomic mass units (1 amu = 1.66 × 10−27 kg). When an uranium atom initially at rest breaks up, the...

Homework Statement There is a monatomic gas held at a constant pressure of P = 1.48-atm, it also has a molar mass M = 16-g/mol and density ρ =1.9 × 10-3-g·cm-3. Find the total internal energy of 1-mol of this gas. Homework Equations U = Q + W E = nCvT PV = nRT The Attempt at a Solution I...

Homework Statement A cylinder contains 0.250mol of carbon dioxide (CO2) gas at a temperature of 27.0∘C. The cylinder is provided with a frictionless piston, which maintains a constant pressure of 1.00atm on the gas. The gas is heated until its temperature increases to 127.0∘C. Assume that the...

A gas in a cylinder with constant pressure, the gas cooled down and its internal energy decreased as well as its volume. The heat Q will be flowing into the gas or out of the gas? My try for the solution: As the volume decrease the work done by the gas will be negative. The gas cooled down, so...

In a trasformation in which P=costant, but internal pressure is different from external pressure, ΔH=Q? I'm asking this question because I know that Q=ΔU+PΔV (where P is the external pressure) and H=U+PV (where P is the sistem pression, so the internal pressure) Am I right?

Edit: @Dale managed to do a far better job in stating the problem, essentially the question is why do we get the same internal energy for different microstates corresponding to a single thermodynamic state Original Post: So I'm self studying a course about thermodynamics and statistical...

I'm a bit confused about the following situation. In a irreversible thermodynamics process the molar heat of an ideal gas changes according to a function of the temperature, say ##c_v=f(T)## (which also leads to ##c_p=R+f(T)##) and I'm asked to determine the heat exchanged during that process...

Hi All, I have a little query concerning the derivation of PV γ = constant. In my textbook of Physics, first they give the equation for adiabatic process using the first law of Thermodynamics, as; dEint = W → (1) where, ΔEint ⇒ change in internal energy and W ⇒ workdone Then, they used...

A uranium-238 atom can break up into a thorium-234 atom and a particle called an alpha particle, α-4. The numbers indicate the inertias of the atoms and the alpha particle in atomic mass units (1 amu = 1.66 × 10−27 kg). When an uranium atom initially at rest breaks up, the thorium atom is...

During gravitational collapse, gravitational potential energy of the gas is converted to its internal kinetic energy so the internal energy of the clous of gas is said to be increased But isn't gravitational potential energy included in the internal energy? Shouldn't the internal energy remains...

Homework Statement There is a pressure volume graph with the gas changes shown, forming a rectangle. The corners are labled A to D starting from the upper left corner heading on to the right until it returns to point A again. The question is at what point, or line is the internal energy of the...

I am wondering if equation $$C_v=(\frac{∂U}{∂V})_T$$ applies only to ideal gases or applies generally for any other system? The second question I have is can we use the following relation: $$dU=nC_vdT$$ in processes that are non isochoric (that is for processes where volume is not constant)? I...

What is the difference between Q=m(u2-u1) + W & Q=m(h2-h1)? Basically I am trying to figure out 2 different sets of questions and apparently using these separate equations yield different answers, and I don't know which equation to use. From my understanding, both of them are used in...

Homework Statement I didn't have enough space to make the topic any more precise. Here is the full question: Express the Internal Energy with Internal Pressure. Homework Equations [/B] This is what I know: the internal pressure is (dU/Dv)T the fundamental equation for internal energy is dU...

What is the difference? I read that thermal energy includes both kinetic and potential energy but isn't that what internal energy is? Cheers!

Homework Statement I was trying to obtain Tds=dh-Vdp by differentiating the internal energy equation U=Q-PV and doing some arrangements but at the end I couldn't achieve my goal.The part that I don't understand is when we differentiate H=U+PV we obtain dH=dU + PdV + VdP and then from there we...